Timeline for Trade-off between hypervolume and diameter of $d$-dimensional shapes having a hypercubic smallest bounding box
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2020 at 16:41 | vote | accept | Penelope Benenati | ||
| Aug 24, 2020 at 11:17 | comment | added | Penelope Benenati | @AlexRavsky your intuition is correct and is explained here: math.stackexchange.com/questions/1996000/… However, it is not clear how to formally exploit this recursion for the final goal of the problem (for instance by using an induction based on this recursion). | |
| Aug 24, 2020 at 8:01 | comment | added | Alex Ravsky | I guess when $1\le r\le\sqrt{2}$ then the intersection is the ball with cut $2d$ hats of height $r-1$, so its volume can be easily calculated. When $\sqrt{2}\le r\le \sqrt{d}$ then the intersection seems to be the cube with spherically cut $2^d$ corners. Maybe there is a way to calculate a volume of such corner too, for instance, by induction with respect to $d$. | |
| Aug 21, 2020 at 0:50 | history | answered | fedja | CC BY-SA 4.0 |